Valid from: Autumn 2022
Decided by: Maria Sandsten
Date of establishment: 2022-10-28
Division: Automatic Control
Course type: Third-cycle course
Teaching language: English
The goal of the course is to give the students a deep and thorough understanding of convex analysis based on Fenchel duality.
Knowledge and Understanding
For a passing grade the doctoral student must Demonstrate deep understanding of convex analysis, in particular: of subgradients and their relation to conjugate functions, the role of conjugate functions in duality, the role of bifunctions for strong duality results, and the connection to minimax optimization of saddle-point functions.
Competences and Skills
For a passing grade the doctoral student must Demonstrate the ability to succinctly summarize the main points of the covered topics as well as to reconstruct the main proofs.
Duality correspondences via conjugate functions Differential theory involving subgradients Constrained extremum problems, bifunctions, and Fenchel duality Saddle-functions and minimax theory Convex algebra
Rockafellar, R. T.: Konvex analys. Princeton university press, 1970.
Type of instruction: Self-study literature review. Course is based on Convex Analysis from 1970 by R. T. Rockafellar.
Examination format: Written report.
The examination is a written report that summarizes all chapters in the book and will demonstrate understanding for how the different results are proven.
Grading scale: Failed, pass